Interaction of fluid interfaces with immersed solid particles using the lattice Boltzmann method for liquid-gas-particle systems

Due to their finite size and wetting properties, particles deform an interface locally, which can lead to capillary interactions that dramatically alter the behavior of the system, relative to the particle-free case. Many existing multi-component solvers suffer from spurious currents and the inability to employ components with sufficiently large density differences due to stability issues. We developed a liquid-gas-particle (LGP) lattice Boltzmann method (LBM) algorithm from existing multi-component and particle dynamics algorithms that is capable of suppressing spurious currents when geometry is fixed while simulating components with liquid-gas properties. This paper presents the LGP algorithm, with several code validations. It discusses numerical issues raised by the results and the conditions under which the algorithm is most useful. The previously existing particle dynamics algorithm was augmented to capture surface tension forces arising from the interface, which was validated for the case of a 2D capillary tube. Using the full algorithm, a particle situated in a region of bulk fluid in an otherwise quiescent situation remained in its original location, indicating that spurious currents were suppressed. A particle brought into the interface of a drop (without gravity) achieved its expected depth of immersion into the drop, demonstrating that all aspects of the code work together to produce the correct equilibrium state when a particle is in the interface. As in an experiment, two particles on a flat interface approached each other due to capillary effects. The simulation approach velocity was faster than that of the experiment, but agreed qualitatively, achieving the same equilibrium state. Given the validations and the favorable, though imperfect, experimental comparison, this algorithm can be a useful tool for simulating LGP systems. The motion of particles normal to the interface can be considered reliable, and the motion tangent to the interface can be considered qualitatively accurate, leading to the correct equilibrium state.